Suppose that f : R² → R² is a linear transformation and that ([:) -[:). (:)-[:] Find a matrix A such that the following equation is true for any vector x: Af(x) = x (In other words, find the matrix associated to the inverse of the linear transformation f. The matrix associated to f satisfies the equation f(x) = Ax instead of the equation above.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Suppose that f : R? → R² is a linear transformation and that
[i]= ([:),
([:) -[:]. ([:)-[4]
f
f
Find a matrix A such that the following equation is true for any vector x:
Af(x) = x
(In other words, find the matrix associated to the inverse of the linear transformation f. The matrix
associated to f satisfies the equation f(x) = Ax instead of the equation above.)
Transcribed Image Text:Suppose that f : R? → R² is a linear transformation and that [i]= ([:), ([:) -[:]. ([:)-[4] f f Find a matrix A such that the following equation is true for any vector x: Af(x) = x (In other words, find the matrix associated to the inverse of the linear transformation f. The matrix associated to f satisfies the equation f(x) = Ax instead of the equation above.)
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